Hi Amaska,
I share your doubts regarding the less-obvious variation names such as SYSUM for example. However I'm not so sure about a possible change/typo/error from SISSON to SISSONS, especially in the early 1800s when general literacy standards were still quite poor, even for the educated classes - just look at the errors often made by some Church Ministers in the PRs. Indeed, just because your Elizabeth thought her name should be spelt a particular way, doesn't mean the Minister used the same spelling for her BMD Parish Records; they only wrote what they thought they heard, in the way they thought was correct, and she probably wouldn't have checked or corrected it.

Only last week I was chatting on a FoD history group on social media about a photo of a man surnamed SARGENT from the 1940s. A lady who was clearly literate and educated thought it might be her relative, but initially doubted this as his surname was spelt slightly different than hers was, and how she thought it should be spelt for her extended family. I then went onto find some BMD records for that man and his brothers, the lady's Uncles, including a few PRs from this website as well as the GRO records. Within those records I found the spelling of this one family's surname varied several times in at least 3 different ways, including for the one same person in PRs at the same FoD church albeit some years apart !
In fact, despite typing their surname several times into the various websites, I found myself forgetting how to spell it consistently, using A's and E's all over the place haha.

Jeff.

PS re embroidery, don't forget that in medieval times tapestries were usually made by the very highest classes, who'd had the benefit of an education of sorts, but I wonder how good their spelling was compared to nowadays, or even if it was consider important to be accurate with such things.

PPS I've tried searching Elizabeth using FamilySearch, which is great at offering spelling variants, and so far struggling to find anyone of that name and approximate birthdate within our general part of the country.

Looking at Freebmd : there are 8 Elizabeth SISSON's marriage listed between 1844 and 1851 in various Counties.

What was interesting to see is the marriage of Eizabeth SISSON (age 20) in 1844 Eye Northampton (District, Peterbro') to John HARD

Elizabeth's surname - written in the copy marriage is written as SIFSON (double SS were usually FS) -

Elizabeth signs her name: Elizabeth SIFSON - however, her father, James SIFSON (as written by the Regisrar) occupation, Labourer, he signs his name: James SISSON.

1851 Census Eye Northamptonshire (Ancestry transcribed as SESSON (in brackets SISSON)